You get an egg from Professor Elm's assistant from any Poke Mart.
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Deposit one of your Pokemon and you may get the egg
In HeartGold, give a Mantine the Wave Incense and breed it. The egg with hatch into a Mantyke.
No, the egg will not be shiny. However, it is possible that the egg will hatch into a shiny Pokemon, but the chances of getting a shiny Pokemon from the egg are not any higher than they would be if the ditto were not shiny.
Give it a full incense and breed it to get a Munchlax egg.
Normal egg groups, same as Diamond, Pearl, Platinum, HeartGold, and SoulSilver.